It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16\ m$ and $12\ m$ in a locality. Find the radius of the new park.

Given: A single circular park equal in area to the sum of areas of two circular parks of diameters $16\ m$ and $12\ m$.

To do: To find the radius of the new park.

Solution:

Let the radius of new park be $r$.

Therefore, Area of new circular park$=$Sum of the two circular park 

$\Rightarrow \pi r^2=\pi(8)^2+\pi(6)^2$

$\Rightarrow \pi r^2=64\pi+36\pi$

$\Rightarrow \pi r^2=100\pi$

$\Rightarrow r^2=100$

$\Rightarrow r=10\ m$

Thus, the radius of new park $10\ m$.

Tutorialspoint

e

Updated on: 10-Oct-2022

31 Views

Kickstart Your Career

Get certified by completing the course

Get Started